The following data pertains to a tension test conducted in a strength of materials laboratory: diameter of the specimen = 15 mm, length of the specimen = 200 mm, extension under the laod of 10 kN = 0.035 mm, load at yield point = 110 kN, maximum load = 190 kN, length of specimen after failure

Question

The following data pertains to a tension test conducted in a strength of materials laboratory: diameter of the specimen = 15 mm, length of the specimen = 200 mm, extension under the laod of 10 kN = 0.035 mm, load at yield point = 110 kN, maximum load = 190 kN, length of specimen after failure = 255 mm, neck diameter = 12.25 mm. Determine: (i) Young’s modulus, (ii) yield stress, (iii) ultimate stress, (iv) percentage elongation, (v) percentage reduction in area, (vi) safe stress adopting a factor of safety of 1.5.

Accepted Answer

We calculate each of the parameters sought one by one.

Area of cross section of the specimen = A [latex] =\frac{\pi imes 20^2}{4}=314.16 mm ^2 [/latex]

(i) At load of 10 kN:

[latex] ext { stress }=\frac{P}{A}=\frac{10 imes 10^3}{314.16}=31.83 MPa [/latex]

Strain corresponding to this load = [latex] \frac{0.035}{200}=1.75 imes 10^{-4} [/latex]

∴ Modulus of elasticity [latex] E=\frac{31.83}{1.75 imes 10^{-4}}=1.81 imes 10^6 N / mm ^2 [/latex]

(ii) Stress at yield point:

∴ [latex] \sigma_{ y }=\frac{110 imes 10^3}{314.16}=350.14 N / mm ^2 [/latex]

(iii) Ultimate stress:

∴ [latex] \sigma_{ U }=\frac{190 imes 10^3}{314.16}=604.78 N / mm ^2 [/latex]

(iv) Percentage elongation:

[latex] \frac{255-200}{200} imes 100=27.5 \% [/latex]

(v) Percentage reduction in area:

[latex] \frac{(\pi / 4)\left(15^2-12.25^2 ight)}{(\pi / 4) 15^2} imes 100=33.3 \% [/latex]

Chapter 2

Q. 2.18

Q. 2.18

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